There are two sets of apparatus of Young’s double slit experiment. In set A, the phase difference between the two waves

Question

(a) There are two sets of apparatus of Young’s double slit experiment. In set A, the phase difference between the two waves emanating from the slits does not change with time, whereas in set B, the phase difference between the two waves from the slits changes rapidly with time. What difference will be observed in the pattern obtained on the screen in the two set ups?

(b) Deduce the expression for the resultant intensity in both the above mentioned set ups (A and B), assuming that the waves emanating from the two slits have the same amplitude A and same wavelength λ.

Answer 1

(a) Set A: stable interference pattern, the positions of maxima and minima does not change with time.

Set B: positions of maxima and minima will change rapidly with time and an average uniform intensity distribution will be observed on the screen.

(b) Expression for intensity of stable interference pattern in set –A

If the displacement produced by slit S1 is

The amplitude of the resultant displacement is 2a cos (ϕ/2) and therefore the intensity at that point will be

I = 4I₀ cos²(ϕ/2)

Ф = 0

∴ I = 4 I₀

In set B, the intensity will be given by the average intensity